why did Jon Arryn choose stannis to take care of his son sweetrobert when that meant he’d be raised with shireen on dragstone by seylse as stannis is always in KL with Lysa and Jon are? Wouldn’t it have been better to have sent him to be a ward or page to his grandfather and a uncle the tullys where he’d be away but with present family and men?
Unfortunately, the primary objective of these arrangements isn't necessarily what's best for the kid's development. This isn't just like picking a school - Jon Arryn's trying to make political connections now and make political connections for Sweetrobin in the future as well. Plus he just wants his son away from Lysa, end of story.
In the near term and the medium term, choosing Stannis as a guardian for Sweetrobin shows Jon Arryn's trust in Stannis. It's a sign of commitment. The two of them are in this together: now, for the next few years, hopefully well into the future, their interests are intertwined.
In the longer term, think of what the end game of Jon Arryn and Stannis' investigation into the parentage of Cersei's children might be. Jon Arryn is sending his son to the next legitimate heir. The next legitimate heir, who has a daughter close to Sweetrobin's age, and no sons. If things go like Jon Arryn's foreseeing them, at minimum Sweetrobin's part of the heir's household. At best, there are a lot of other avenues for advancement.
Would Sweetrobin get a better education at Riverrun? Maybe, maybe not. Would he get better socialisation at Riverrun? Almost certainly. Would Jon Arryn perceive sending Sweetrobin to Riverrun as more likely to be amenable to Lysa, easier on her to deal with? Quite possibly (he'd be wrong if he did).
But he's not after the best education and best social development for Sweetrobin, nor what's best for his family's emotional life. He's after the best all-round deal, which he appears to believe is removing Sweetrobin from his mother and getting him in good with the powerful lord Jon Arryn believes to be Robert's current legitimate heir.
